precalculus

[dull rain]

Ahh...yes you're right...

But if I also put a condition that both polynomials should have their coefficient of highest power of x = 1, then?

[willow bear]

ah, so you're making them monic, ok. so that means that in principle such a formula exists

but i would imagine it to be quite nasty!

[scarlet idol]

guys

would the limits be 2 and -2

or something else??

??

[amber badger]

can someone help me change this equation to polar

i got r(cos+sin) = 0

and I think it is wrong can someone help me

[viscid thistle]

try pinging helpers

i mean i do not know how to do that so i cant help bro. but other helpers can.

[grizzled osprey]

can someone walk me through this?? just learning it

[granite stream]

honestly just learned this as well but I believe it would be (-7, -4] because -7 < x is a open dot on the number line meaning we should use a parenthesis whilst x<=-4 is a closed dot on the number line meaning we should use a bracket

when the x is greater than or equal to we use a bracket and same with less than or equal to

[opal tree]

Yeah

Although I'd rather have it clarified that x is within a set of all reals

And then go into the specifics

[granite stream]

yeah

[lofty wing]

yes ofc

[inland ferry]

can someone help me please

[charred viper]

Are the last two relations even correct?

You don't know whether (x-3) will be negative or positive, can you really group it like |x-3|^2?

For all we know it can be -|x-3|^2 no?

[summer ruin]

they're wrong, but for a different reason

$|x+y| \leq |x| + |y|$, hence $|x-3||(x-3)+6| \leq |x-3|^2 + 6|x-3|$

[obsidian monolith]

Transparent_Elemental

[summer ruin]

but $|x-3|^2 = (-|x-3|)^2$

[obsidian monolith]

Transparent_Elemental

[charred viper]

ohh i seee

so it should've been a less than or equal to signn

thxx

[winter crater]

Can someone help me

[amber surge]

can I get some help im very confused

[proud raven]

oh man i gotta check this channel more

[twilit rivet]

how do u find the inverse of

[tall elbow]

You just replace y with x i think

[frank vine]

Reply x with y and vice versa then solve for y and you have inverse function

[upbeat rover]

that's what I thought, and the rearange to isolate y on one side

[viscid thistle]

But y is already on the left alone if you swap

[tidal perch]

solve for y

[sick heron]

can anyone help me with an issue im having?

So im watching 3blue 1 browns first video on the essence of calculus, and i got all of it until he gave a formula for the approximation of height for a tiny sliver of dx

so essentially its (x2)-(x1)/the difference of the top = x^2

so for example you could choose a point 3

and add a little nudge, say 3.001

so you subtract those, and you get .001, so its (3.001)-(3)/(.001) and that some how equals 3^2?

ok im kinda getting it more

wait so it has to be A(x2)-(x-1)/the difference?

[vapid plaza]

[ A(x2) - A(x1) ] / (x2-x1) will be slope of the secant line

[fleet tendon]

??????

[fleet tendon]

Nvm i just did it

This is the actual most beautiful equation

[signal tusk]

does anyone understand this?

[tacit pelican]

8200*1.06^x + 9.75x?

[signal tusk]

the x is an exponent?

[ruby comet]

Yes

[mellow vigil]

isnt it $e^{i\pi} + 1 = 0$

[obsidian monolith]

NotMyself

[graceful kiln]

so confused someone help?

[mellow vigil]

just put the values for x

in f(x)

$f(-4) = -3(-4)-4
=12-4=8$

[obsidian monolith]

NotMyself

[graceful kiln]

ik this but idk how tho

[mellow vigil]

$f(x) = -3x-4$

[obsidian monolith]

NotMyself

[mellow vigil]

You replace the value of x with input

then calculate

so if u take input(x) as -4

then write-3(-4) -4

then calculate

[graceful kiln]

i will try

thank you

[mellow vigil]

np

@graceful kiln also i think u should ask questions about function in #prealg-and-algebra

cuz its algebra ig

[graceful kiln]

oh alright thanks

is this correct?

[willow bear]

f(-2), f(1) and f(5) are incorrect

[mellow vigil]

^

[graceful kiln]

still can't find the answer lmao

[mellow vigil]

its basic arithmetic

just substitute the value

[graceful kiln]

it's new to me but alright

[mellow vigil]

when u get the concept its just easy calculations with these type of questions

[graceful kiln]

alright i got it now

thank you

[mellow vigil]

np

[graceful kiln]

@mellow vigil can i get some help

it's alright if u don't want to

[mellow vigil]

um i havent yet got to domain and range

so i also dont know

[tacit pelican]

if a function maps the same input to different outputs, it is not a function

[sly ocean]

raise both sides to the power of π and you'll get the famous equation

[fleet tendon]

Not anymore!

[mellow vigil]

when and why?

[jolly umbra]

Can someone help me with this please?

[willow bear]

@jolly umbra do you know the definition of average rate of change?

it's $\frac{f(b)-f(a)}{b-a}$. the problem is rather plug-and-chug if you know that that fraction is the avg rate of change of $f(x)$ from $a$ to $b$.

[obsidian monolith]

Ann

[jolly umbra]

hmm ok

thanks

[sterile turret]

a

[misty harbor]

Pre calculus is related to differentiation right?

[surreal berry]

everything before differentiation

[wraith coral]

Hey I have a question, I had a problem Find the sum of the first 37 terms of the following series, to the nearest integer.
10, 14,18,...

The answer I got was 3034 can someone check it for me and tell me if it's right or wrong you don't have to give me the answer.

[viscid thistle]

Precalc is technically Trig

trig is usually called precalc in USA

[wraith coral]

@viscid thistle Do you mind checking to see if 3034 was what I was supposed to get?

[opal tree]

No we usually have trig as a separate thing

Group it with algrebra ii

So it goes from Algebra II and Trig to Precalc

[viscid thistle]

Hi I'm new here, does this server have tutors?? specifically pre-calc for me?

[hushed sphinx]

No.

The server has people who hang around in their spare time and sometimes answer questions and/or give homework advice in the channels when they feel like it.

The #❓how-to-get-help channel contains a description of the system.

[viscid thistle]

oh ok, thank you for the advice

[viscid thistle]

umm, i never knew that even though i live in usa and attend a IB school.

yeah in IB School they call it precalc for full year trig.

[opal tree]

Probably because you attend an IB

Might also differ state to state

[viscid thistle]

right.

[viscid thistle]

let me try

[viscid thistle]

yes u are correct

[wraith coral]

Thank you

[potent acorn]

Somebody can you please answer this 😀

[vague sparrow]

While asking questions, make sure to mention all relevant details, including what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.

[fleet tendon]

Why

Why do you need to multiply by g’(x)

Does it come from derivate definition? Or is it smth else?

I looked up on yt but all i find are just examples

And im too lazy to do it by definition rn

[hushed sphinx]

First off, that is calculus, not precalculus.

Everything is ultimately from the definitions, of course.

Intuitively you could think of x increasing with time at a constant rate. Then g'(x) is the rate the input to f increases with, and if the input to f increases twice as fast, then the output will also increase twice as fast even if f itself is the same function.

[fleet tendon]

Huh

I saw derivates in precalculus

[hushed sphinx]

Derivatives are the definition of what calculus is about.

[fleet tendon]

Moving to #calculus

[lilac onyx]

help

guys

plz help

my mom said shes taking my ps4 if i dont get my grade up in pre cal

😭

i beg

[hushed sphinx]

What are your thoughts about the question? Do you know what the words in the answer options mean? If not, look them up.

[lilac onyx]

PLEASEB RO

I JUST NEED THE NASWER

i have 1 last answer chance

[hushed sphinx]

If you want better grades, then you don't need answers. You need to understand the material; answers and grades will then follow automatically.

[lilac onyx]

damn

thast true

facts facts

thank you troposphere for your advice

[hushed sphinx]

I detect sarcasm here, but that's the deal. People here will happily try to clear up uncertanties and misunderstandings you have, but "I just need the answer" is not going to make anyone want to engage with you.

So the first step in getting useful help is to actually describe enough of your understanding of the question that someone can figure out what knowledge or understanding it is you're missing.

[rustic swallow]

I need help with this problem

[mellow vigil]

just replace the values for x

[sick quartz]

A function maps one set of values to another. You've got g(x). You choose a value of x, say x =2, and the notation becomes g(2). Wherever there's an x on the right hand side of the = sign, you put 2. And this gives you the number that x = 2 is mapped to.

[maiden crest]

y’alll I neeed helppppp… we were asked to make a video abt facts of circle conic sections…. But we can’t cover the PI and equations of a circle coz we already discussed it… I don’t rlly know what to do coz there’s nothin much to talk about anymore

[lost grove]

show the pi=4 proof and show why it's wrong

it has to do with pi

but not anything about properties of pi

[maiden crest]

but that kinda goes far from our topic😅 I was gonna go for how Circle became related to pi but my friend already went for that😌

[lost grove]

hmm

show the sphere surface area proof

for 4pir^2

the one with the cylinder

[maiden crest]

awesome concept but it’s a sphere😅 not rlly about conic sections anymore

Ig i’ll just find another way how to talk abt pi

thanks for the help thoo

I rlly appreciate ur suggestions!

[mellow vigil]

https://brilliant.org/wiki/conic-sections/

Maybe this might help

also try adding some history about conic sections

[maiden crest]

rightt i’ll just go with history.. thanks!

[fierce minnow]

Range of the function

[dark niche]

D(f)?

[solar olive]

It is negative and increasing, pretty obvious

[solar olive]

$x \in \mathbb{R}$

[obsidian monolith]

Impractical

[solar olive]

fuck

ok

the (x^2 + 1)^2 (x^2 + 3) is always guaranteed to be positive

even if its not, its gonna be cube-rooted later and its defined

Wait i forgot about the denominator being 0, woops

Nvm, the denominator is always positive too (u could verify this by realizing the x^2 part is always positive, or u could calculate its discriminant)

[fierce minnow]

That's the domain i guess not the range

How to calculate it

[solar olive]

Oh right, for range u probably could find its minimum/max

[fierce minnow]

I am unable to help me

[solar olive]

find its derivative

although that seems kinda overkill

[summer ruin]

you'd also need to analyze if there are asymptotes and how function behaves for x-> +-inf

[solar olive]

considering this is a precalc material

[solar olive]

There are no asymptotes

[fierce minnow]

No it's range

[solar olive]

Anyways after analyzing the limit for +inf and -inf, both are 1/3 so the minimum is 1/3

the next step is to find the maximum

[dark niche]

E(f)?

[solar olive]

And since the function seems to be going up and down im just gonna cheat and just find the value when x = 0

• i dont think u would actually use derivatives in precalc

putting x = 0 results in 3^(1/3) / 4

so i think the range should be 1/3 < y <= 3^(1/3)/4

Actually nvm im wrong

the derivative for hte original function is -((2 x (-1 + 2 x^2 + 3 x^4))/(
3 ((1 + x^2)^2 (3 + x^2))^(2/3) (4 + 3 x^2)^2))

solving for 0 results in {0, pm sqrt(3)/3}

plugging either + or - sqrt(3)/3 to the original function results in $\frac{2}{3} (\frac{2}{5})^\frac{2}{3}$

[obsidian monolith]

Impractical

[solar olive]

Which matches the mathematica result

[wise spoke]

How ya solve this?

i tried to assume $x^x$ as a but that just doesn't give me an answer in proper form

[obsidian monolith]

∫Inheritanc-e ♦

[fierce minnow]

Okay you did something i don't what but you did something

[night flame]

Can someone help solve this problem/equation? (This is my first time taking pre cal by the way.)

[dark niche]

HA? SA? VA?

the what

[night flame]

All three.

I think the vertical would be - 5…

I don’t know actually.

[dark niche]

[vital torrent]

https://gyazo.com/370ed9ab90af6647d65975ed333c7ac0

need help with the last one, i also did (-x^2)+9 over 10

didnt work

[uncut mulch]

you didn't sub in -x correctly

recall how you did h(-3)

[vital torrent]

ah i see, thanks

[night flame]

😅😅

[north kraken]

How do I change the formula for the curve of the line y=x^2 fall towards the y axis?

...on the positive side

[grim ice]

Like stretching/Shrinking?

[north kraken]

I think I am looking at a cubic graph. y=x^3

It won't stretch but it will flip over so that increases more towards y

The only graph that I have found that has that on the positive x is; y = -0.2(x-3.6)(x - -2) but it is limited until about x=2 then begins to decrease

[north kraken]

The best I could find is something like y=-(0.08x-2)^(4)+10

Problem solved

[viscid thistle]

Hi can someone solve this without calculator? log(48)

[hushed sphinx]

Someone probably can to a few significant digits, by remembering logs of 2 and 3.

[brisk pasture]

I'm confused can someone help

[tough cargo]

I think the answer is 4x/(6x+1)

[brisk pasture]

How?

[tough cargo]

It’s basically 2/((1/2x)+3)

And you simplify it

[brisk pasture]

Oh I think I got it thanks

[tough cargo]

No problem

[brisk pasture]

@tough cargo so 2 x (2x/1) = 4x

So you left with 4x/2x/1+3 (2x/1)

You multiply 2x and 3, then get 6x and add the 1?

[knotty zephyr]

how do u solve this problem?

does that mean that the vertices are (0, 20) and (0, 20)

I'm confused, what does it mean when the length of is 4/5 of the length of the minor axis???

also how do u find the "b"?

[obsidian monolith]

Amer

[signal gorge]

is that true when finding limits?

when both x--> infinite

[willow bear]

no

these functions are not equal and not even their limits as x -> +∞ are equal.

[signal gorge]

the first one is 2

and the second one is 2? because both in the frac are equal

[willow bear]

no

$\lim_{x \to +\infty} \frac{2 + \ln(x)}{1 + \ln(x)} = 1$, not 2.

[obsidian monolith]

Ann

[signal gorge]

is it because it's undefined?

[willow bear]

"it"?

what are you talking about?

[signal gorge]

can't just rule out ln(x) togheter

[willow bear]

what do you mean?

ln(x) is the dominant term in both num and denom. of course we can't rule them out!

[signal gorge]

$\lim_{x \to +\infty} = \frac{2 + +\infty}{1 + \infty}

$\lim_{x \to +\infty} = \frac{2 + +\infty}{1 + \infty}$

[obsidian monolith]

Amer

[willow bear]

with all due respect

what the hell are you talking about

[cyan jolt]

it's undefined infty/infty

that's why we have to do something with it to get rid of undefined

[signal gorge]

$\lim_{x \to +\infty} \frac{2 +ln(x)}{1 + ln(x)} = \frac{2 +\infty}{1 + \infty}$

[obsidian monolith]

Amer

[willow bear]

yes, plugging in x=∞ as-is to (2 + ln(x))/(1 + ln(x)) gives (2 + ∞)/(1 + ∞).
yes, that is ∞/∞.
yes, ∞/∞ is an indeterminate form.
no, that alone does not mean anything other than "do more work".

[signal gorge]

oh yes that's true

BTW this #help-16 message i didn't know how to use it
i did solve it using another way but i couldn't find a way to solve it using that one

[cyan jolt]

divide by ln(x), then (2/ln(x)+1)/(1/ln(x)+1)=(0+1)/(0+1)=1

I read what you typed before, it's not how mathematics work with indeterminate form

Just read how to work with this symbol ∞

∞ is not real number

it's special symbol made up by mathematicians

[mellow vigil]

how do u use symbols in text without using Texit

[cyan jolt]

I copy paste from Google usually or other posts

[mellow vigil]

oh ok

[signal gorge]

$\lim_{x \to +\infty} ln(e^{-x} + 1) = +\infty$

[obsidian monolith]

Amer

[signal gorge]

can anyone explain pls?

[willow bear]

well we can't explain 2+2=5 to you bc it's false

and so is this statement

ln(e^(-x)+1) approaches ZERO and not infinity

@signal gorge

[signal gorge]

it's a mistake ig

imagine putting this in a book for over 300k students yearly

[signal gorge]

$f'(x) = {-e^{-x-1}}{e^{-x} + 1}$

$f'(x) = \frac{-e^{-x-1}}{e^{-x} + 1}$

[obsidian monolith]

Amer

[signal gorge]

f'(x) can't be equal to 0 right?

because i did this $\frac{-e^{-x}}{e^{-1}}{e^{-x} + 1}

[obsidian monolith]

Amer

$\frac{-e^{-x}}{e^{-1}}{e^{-x} + 1}$

[signal gorge]

$\frac{-e^{-x} e^{-1}}{e^{-x} + 1}$

[obsidian monolith]

Amer

[tulip badge]

I solved the problem following the teacher's example, but nothing worked out for me, so I decided to start with the teacher's example. please tell me why she has no minus in the remainder of the division of polynomials by a continued fraction?
photo of an example of a teacher, and below is a photo of the solution of the first division

[real bane]

Does anyone have a program for the ti-84 that has a solver and steps for the equations for pre calc

[brisk pasture]

Should this all go in calculus?

Btw it's undefined

X can be all real numbers

[strange echo]

it's asking "as x approaches +inf, what does f(x) approach?"

[viscid pilot]

Can someone tell me what would be the steps to solving this?

[hushed sphinx]

This seems to require maximizing a cubic polynomial -- I'm not sure how one would do that with precalculus tools.

[echo lava]

Hi guys, im not sure if this question fits this channel but here goes

why is the height of the runner divided by 2?

[vapid plaza]

The question assumes the centre of mass to be at the “centre” of the runner’s body.

So, the distance between the contact point on the floor and the centre of mass is h/2

[echo lava]

OH that's makes sense, thanks so much :))

[pale violet]

Have I done this correctly? (Sorry for posting this in precalc but I asked in algebra twice already and still have not gotten a response.)

[hushed sphinx]

Solution verification is tedious, boring, mostle thankless work, and it's not really surprising when nobody is volunteering for it.

[lament anchor]

can anyone help me with the highlighted questions

[split fractal]

can someone help me with this

[summer ruin]

find all x and y that satisfy two given inequalities

[plush stag]

can someone help me with this

[viscid thistle]

Should I feel bad that I am taking precalc and I love math and I dont get this

[sick quartz]

as x approaches infinity

[grave zodiac]

Hey how do you approximate the instantaneous rate of change over an interval

[vapid plaza]

take 2 points from the interval (possibly endpoints of the interval? ) and calculate the slope of the line passing through them

[zenith halo]

have you heard of a derivative

[sick quartz]

instantaneous rate of change over an interval?

find the derivative

[viscid thistle]

Anyone who may be able to help relating to pre calc in #help-23

[torpid linden]

If one of the vertices of the hyperbola is the origin while one of the endpoints of the conjugate axis is at (3,-9), how far is the focus from the center

[viscid thistle]

no, u just need practice

[grave zodiac]

Without finding the derivative

[sick quartz]

i don't want to speculate. so can you send the problem?

like a ss

[grave zodiac]

Yea sure

@sick quartz

[viscid thistle]

Does it say don't use derivatives?

[grave zodiac]

My teacher said

[sick quartz]

for the first part, they're asking for the Δy/Δx

[grave zodiac]

Yuh

Ik that part

[sick quartz]

and the second the dy/dx evaluated at the leftmost x they provide

[hushed sphinx]

The second part doesn't even mean anything without derivatives.

[sick quartz]

and using instantaneous automatically implies derivatives

[grave zodiac]

He said to get an approximate value

[viscid thistle]

Then you just have to approximate right? So find the delta y /delta x of really small changes.

Like

For the first one use 0.99 and 1.01

[sick quartz]

then they would ask to approximate

[hushed sphinx]

It doesn't make sense to ask you to find a derivative without using derivatives.

[grave zodiac]

So F(a+0.0001)-f(a)/a+0.0001-a

[sick quartz]

maybe newton's method?

[warm vale]

it likely wants you to draw tangent lines on the paper

[viscid thistle]

Yea that should approximate it. Ask your teacher once which method to use

[grave zodiac]

Alright

My teacher said to use 0.0001

[viscid thistle]

bruhh i got no clue on how to do this

is it just d+c=

[summer ruin]

it's not

$(a+b)^2 = (a+b)(a+b)$

[obsidian monolith]

Transparent_Elemental

[viscid thistle]

ye but how do i even apply that formula

[summer ruin]

replace a with c, b with sqrt(d)

[buoyant patrol]

Transparent elemental

Is it possible for u to help me with econ

[summer ruin]

no

[viscid thistle]

ty

[buoyant patrol]

Oh

Who’s

Good at

Econ

I meant like can teach

Cause I’m stuck

With this paper

[vapid plaza]

This is math server

[buoyant patrol]

Can u help?

[vapid plaza]

No

[mellow vigil]

Go to Public Servers > Type "Economics" > Join one of them > Ask there

[buoyant patrol]

Is there no one that can help

[mellow vigil]

maybe ask in #discussion atleast not in #precalculus

[viscid thistle]

would it be smt like this?

[summer ruin]

why is there sqrt(d)^2

[mellow vigil]

why would you do that

[obsidian monolith]

NotMyself

[mellow vigil]

just use d

[viscid thistle]

oh bruh

didnt even realise that ty

[mellow vigil]

np

[viscid thistle]

so thats the answer then?

[mellow vigil]

no simplify it

use the formula

[obsidian monolith]

NotMyself

[viscid thistle]

wth i used a difernt one

lol

[summer ruin]

if you do the multiplication correctly you'll see that $(a+b)(a+b) = a^2 + 2ab + b^2$

[obsidian monolith]

Transparent_Elemental

[viscid thistle]

the difference quotient

[cosmic girder]

ehhhh no

[mellow vigil]

why?

[cosmic girder]

sqrt(a^2) is always positive

a can be both positive and negative

[mellow vigil]

they can put it later on

[cosmic girder]

sqrt(a^2) = abs(a)

[mellow vigil]

after solving it

[cosmic girder]

that's not how it works lol

,, \abs{x} = \sqrt{x^2} \neq x

[obsidian monolith]

illuminator3

[mellow vigil]

oh

didnt think that

[mellow vigil]

sry dude

[mellow vigil]

do as u were doing

[mellow vigil]

cuz of this

[viscid thistle]

i quit that a while ago

lol

[tough bronze]

Hi! So I have a lil problem here. So I have this problem below, and my teacher wants us to find the maximum. Obviously you can simply do -b/2a, but she wanted us to see if we can solve it in an intuitive way and figure a solution out ourselves. So I thought "well x is just a variable obviously, and when it goes up 1, it constantly increases by 800 as per the 800x. so this, it would peak when the shift from 10x^2 to 10(x+1)^2 occurs where the difference between the two is equal to 800, because any further beyond that and the -10x^2 would grow faster than the 800x would and shrink the graph exponentially" But I'm plugging this into mathway and as 10x^2-10(x-1)^2=800 and i am getting 40.5, but the answer is exactly forty. I am so close so i feel it is something minor, but what am i doing wrong?

im stumped

well i got a little hint, but i cant really decipher it

when i plug in 10(x+1)^2 - 10x^2 = 800, i get 39.5 instead of 40.5. the answer is 40 mind you, right smack dab in the middle

I dunno what to make of that, but i think i was on the right track with the concept at least

[summer ruin]

finding maximum of $-10x^2+800x$ is the same as finding maximum of $-x^2 + 8x$ because you could just divide everything by 10, this is kind of like units conversion

[obsidian monolith]

Transparent_Elemental

[summer ruin]

you could then factor it and think for which values of x you get product maximized

it's also useful to know that you can always have a problem $\max f(x)$ which is equivalent to $\min -f(x)$, it's fairly intuitive if you think about it

[obsidian monolith]

Transparent_Elemental

[balmy kernel]

,w 9/3^2

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Charliee#8776

[balmy kernel]

-4^2

,w -4^2

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Charliee#8776

[balmy kernel]

?

[hushed sphinx]

#bots please.

[tough parcel]

How do you do this?

i know how to do it, and so far i got: (3hx^2 + 3h^2x + h^3 - 3x)/h

but you can't do anything else

[split holly]

how does the limit approaching from the right have a value, but the limit from the left does not exist?

[summer ruin]

the root is undefined

[proud raven]

,w expand (x+h)^3 + 3(x+h)

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by jan Niku#2119

[proud raven]

are you sure?

[craggy torrent]

How can i solve this? i tried factorization but didn't work

[dire forge]

limit doesnt exist at x=2

[craggy torrent]

thanks

[dire forge]

double check by putting it into desmos

[craggy torrent]

does this indicates limit at 2 doesn't exists? sorry im new to this topic

[summer ruin]

limit at a point doesn't exist if right side and left side limits aren't equal

[craggy torrent]

i see, after checking the graph it turns out that y is undefined when x = 2, thanks

[summer ruin]

no, that doesn't really give you any insight into whether the limit exists at a point or not

$y = \frac{x}{x}$ is undefined at $x = 0$, yet it's right side limit at 0 equals it's left side limit and they're both equal to 1, therefore the limit at $x = 0$ exists and is also equal to 1

[obsidian monolith]

Transparent_Elemental

[craggy torrent]

ohh so the graph actually indicates limit exists at 2 cause y at x=2.00..1 is equal to y at x=1.99..9

thanks again

[summer ruin]

no, the limit at x=2 doesn't exist

[craggy torrent]

i mean x->2

[summer ruin]

yeah that doesn't exist

left side limit is -infinity, right side limit is +infinity, they're not equal therefore limit as x->2 doesn't exist

[sullen saddle]

can someone help me with this?

[signal gorge]

what am i doing wrong?

i've been told the answer is incorrect

[signal gorge]

try P1P2 = 3.P1P

[willow bear]

,calc (3-2i)^3

[obsidian monolith]

Result:

-9 - 46i

[willow bear]

ah, yes

(-2i)^3 is not 4

it's 8i

27-36+4 isn't -4 either

@signal gorge

[sullen saddle]

what does this mean?

[signal gorge]

actually P1P2 = 4.P1P

[sullen saddle]

what does the 4 symbolize?

[signal gorge]

i'm confused, let me write it down

it might be wrong though

[signal gorge]

,calc -(1-i)(3-2i)^2

[obsidian monolith]

Result:

7 + 17i

[sullen saddle]

thank youu

[heavy sinew]

Hey guys, who knows if u can add or subtract variables in a complete the square problem

[hushed sphinx]

What is the problem and what do you want to do?

[heavy sinew]

I am getting the notebook

-x squared, +x, -1

and I have to complete the square

[hushed sphinx]

Huh? Is "notebook" a translation from some non-English language here?

[heavy sinew]

no, it is english

the thing with the lines, and paper where you write in it

or the blue lines on white paper

[hushed sphinx]

I am very confused.

[heavy sinew]

the blue lines on the white paper that you write in that has the problem on it

[signal gorge]

try to multiple by -1 maybe

[heavy sinew]

I tried that, but I couldn't get it to work

instead, I just did a complete the square, and added, or subtracted x

[signal gorge]

$x^{2} + bx + c = (\sqrt{x^2} + \sqrt{c}$

$x^{2} + bx + c = (\sqrt{x^2} + \sqrt{c})$

[obsidian monolith]

Amer

NotMyself

[heavy sinew]

what about the principle root

?

[signal gorge]

nvm mine is wrong i can't delete it

[mellow vigil]

Why are there so many notations for Symmetric differences between 2 sets

[obsidian monolith]

NotMyself

NotMyself

NotMyself

[mellow vigil]

Which one should i use?

[willow bear]

definitely not the last one, that's difference not symmetric difference

also perhaps you meant $\oplus$ and not $\ominus$?

[obsidian monolith]

Ann

[willow bear]

tbh it doesn't really matter which one you use, so long as both you and whoever reads your work is aware of it.

[mellow vigil]

ok

[mellow vigil]

i didnt knew about oplus

[mellow vigil]

idk this article says that

https://byjus.com/questions/what-is-the-symmetric-difference-of-sets-a-and-b/

[willow bear]

the title says symmetric difference but then it talks about non-symmetric difference lmao

would not trust this site generally if i were you

[mellow vigil]

the thing is this site is the most reputable site among students in my country lol

[willow bear]

please don't reply-ping me so often

[mellow vigil]

oh ok sry

[signal gorge]

i was trying to sketch f(x) = 1/x - 1 - ln(x)

but i found out that when f'(x) = 0 that x = -1

what do i do? i know there can't be negative in ln(x)

[mellow vigil]

The zero of f(x) isnt equal to -1

[obsidian monolith]

NotMyself

[mellow vigil]

You can check also

1/1 -1 -ln(1) = 0-0 =0

so you can make the graph actually

[uncut mist]

I have ran into a slight confusion I keep making the wrong step in finding the zeros of a trinomial funciton

[mellow vigil]

what do you do wrong

[signal gorge]

i mean the derivative of f(x) = 0

[mellow vigil]

oh ok

[obsidian monolith]

Amer

[mellow vigil]

idrk about derivatives

[signal gorge]

$\frac{-1-x}{x^2} = 0$

[obsidian monolith]

Amer

[signal gorge]

i find the answer x = -1 am i doing something wrong?

[visual hill]

can someone help me solve this

i have no idea how to start

[summer ruin]

express each function using sine and cosine

[visual hill]

could u work on out so i can see exactly what you mean by that

[summer ruin]

$\cot (x) = \frac{\cos (x)}{\sin (x)}$

[obsidian monolith]

Transparent_Elemental

[visual hill]

so do i plug in -3pi/4 inside cot(x)

[summer ruin]

there's no cotangent on your question

express each function using sine and cosines first

[visual hill]

im not sure how to do that

[summer ruin]

well you should know how each of these functions can be expressed using sines and cosines

otherwise you can't really answer that unless you memorized the entire trig table for values of sec(x), csc(x), etc

[sonic arrow]

I had very basic question about the norm of vectors.

can you do something like
$$
\frac{|\vec{a} \cross \vec{b}|}{c} = |\vec{a} \cross \frac{\vec{b}}{c}|
$$

[obsidian monolith]

hexaGone

[sonic arrow]

is that legal or will I go to jail if I do that

also c > 0

[summer ruin]

use the definition of cross product to see if it's true

[sonic arrow]

Ok so:

From the definition of the cross product we know that $|\vec{a} \cross \vec{b}| = |\vec{a}| \cdot |\vec{b}| \cdot \sin\theta$ where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$.

Dividing that by a scalar $c > 0$ results in $|A| \cdot \frac{|B|}{c} \cdot \sin\theta$.

Now the only way that this would be equal to $|\vec{a} \cross \frac{\vec{b}}{c}|$ is that the angle between $\vec{a}$ and $\frac{\vec{b}}{c}$ is the same as $\theta$. Which, I think, means that $\frac{\vec{b}}{c}$ is on $\vec{b}$.

But I'm not sure if that's true or not

[obsidian monolith]

hexaGone

[summer ruin]

if you stretch a vector, does it change it's orientation?

[sonic arrow]

I mean it makes sense because of similar triangles

but I'm not sure and maybe a little bit too lazy to try to show it

[sonic arrow]

I don't think so

[summer ruin]

well there's your answer

[sonic arrow]

ah ok then

thanks

[sonic arrow]

It does make sense that way actually. Since the x value and y value are all divided by c and the triangle is right angled then all such triangles made by scalar multiplication are similar. Therefore the angles don't change.

[alpine wraith]

Not my homework but

I figured this must have a formula of some sort to get an answer?

My friend said their teacher said only guess and check works

Surely it doesn’t?

[raw hill]

sum of a geometric series

[alpine wraith]

care to write it out?

just out of curiosity

I don’t really do series

[opal prism]

HELP

Ok so how to use digits 0 to 9 at most one each time and make a true equation distributive property it looks like #/#(#y+##)=#y+#

[willow bear]

why did you bold your entire message?

so you're asked to fill in the blanks in $$\frac{\square}{\square} (\square y + \square\square) = \square y + \square$$ in such a way that each blank is filled with a single digit and no digit is used twice, yes?

[obsidian monolith]

Ann

[opal prism]

Yesss

[vapid plaza]

||3/6(4y+18)=2y+9|| seems to work

[opal prism]

THANK UU

Xoxoxoxox

[nova grove]

can someone help me with 3a

[viscid thistle]

thanks wow, That was so beautiful

[terse ore]

could someone help

[viscid thistle]

can anyone help me with a few problems

[chrome nova]

$(\pi-2x)tan(x)$

[obsidian monolith]

BoopySnooty

[chrome nova]

how do i evaluate the limit of this as x approaches pi/2

[chrome nova]

im gonna be honest i could never think of a solution like that

well done dude

thank you @mild orbit

[mild orbit]

you're welcome. You have to use change of variable 😉

[lone gull]

Hello everyone

I’m struggling a lot with maths

I study too but I can’t see to do well

Here’s my test can you guys help me on what to study because it looks like I can’t understand anything atp

[viscid thistle]

can anyone help me solve this

[mild orbit]

348.08

[viscid thistle]

@mild orbitoh i just did that problem and got it wrong can u help me with another one

[mild orbit]

yes, of course

[viscid thistle]

@mild orbit

[mild orbit]

199.22

[viscid thistle]

@mild orbit Professor Jorge is there a way you could help me with 5 problems it would mean the absolute world to me

[mild orbit]

ok 👍

[lone gull]

Can anyone hep me figure out how #7 is wrong?

Also what do I do for 8? And 9

Please I just want to know if they are right

[storm frigate]

can anyone explain, to me how does the one I incircle impact my answer

[uncut mulch]

in the line directly below

the full half angle formula is
$$\sin\br{\frac{\alpha}{2}} = \red{\pm} \sqrt{1 - \cos{\alpha}}{2}$$
where the sign depends on the quadrant of $\frac{\alpha}{2}$ \
since $\frac{\alpha}{2}$ is in quadrant 1, they're using the positive case.

[obsidian monolith]

ℝamonov

[storm frigate]

Ahh i see...so since it is quadrant 1, is it all positive?

Ty ty

[sullen saddle]

how do i solve this?

[willow bear]

a good first step would be to find the center and radius of the circle

[sullen saddle]

after i find the circle and the radius, i find the slope from the circle and the points?

[lyric plinth]

cool

[limber elk]

would this be implicit differentiation maybe?

[hushed sphinx]

Probably not if it's supposed to be "precalculus". But it should be straightforward enough to complete the squares to find the center of the circle, and then the tangent is just perpendicular to the radius.

[limber elk]

ah right

good point

[opal tree]

Implicit differentiation

But this is #calculus

[hushed sphinx]

That seems to be a very popular strategy :-)

[chilly glade]

Where am I going wrong here? It’s looking like I’m going to come out with an imaginary number but we have not gone over those in class

[summer ruin]

the equation has no real solutions

though you should've also checked that the solution must satisfy $x^2 -6x > 0$ and $x-30 > 0$

[obsidian monolith]

Transparent_Elemental

[chilly glade]

Thanks!

[viscid pilot]

how would I solve for B here?

[summer ruin]

determine all p such that D(p) > S(p)

p >= 0 of course

[tulip lily]

I thought that this was precalc

This kinda seems like calc1 to me

[raw hill]

where is the calculus

[viscid thistle]

so Calculus is in the Civil Service Exam? I did not know that buddy. Well, which country's civil service are you referring to?

[raw hill]

It's a complicated disaster that's an inside joke with my irl friends

Let's just say that lol

[viscid thistle]

oh ok. well nice to know

[kindred sluice]

Wondering if I can get a hint as to how to verify this identity. Ive tried a few different approaches but have been stuck for quite a while

[deep marsh]

hope its readable

[kindred sluice]

oh crap you made that look easy

thanks

I always get messed up when trying to figure out what identity to reintroduce back in

[kindred sluice]

wait through isnt sinu = root(1-cosu)

[deep marsh]

yes

[deep marsh]

cos^2u

root(1 - cos^2(u))

[kindred sluice]

oh wait I think i see

after the distribution

we get the answer

[lone gull]

I need help with #11

#10*

I don’t know how to rewrite it

[harsh harbor]

how do you do this?

[grizzled osprey]

could someone help? i’m a little confused.. i got it down to 2y squared + y + 15 over (y+5)(y-1) (i think that’s right) but i don’t remember how to further simplify that ..

[hushed sphinx]

Divide both numerator and denominator by x^4.

[hushed sphinx]

There's not really anything more to do from that point.

[harsh harbor]

so it equals 0?

[hushed sphinx]

Yes.

[harsh harbor]

so that means dne?

@hushed sphinx

[proper garnet]

long story short i transferred into precalculus very late into the quarter and now need to catch up

[glossy lichen]

Do you understand how functions work? @proper garnet

[hushed sphinx]

The number 0 definitely exists.

[nova thorn]

anybody got time to go into a call real quick on paint 3d?

its a short problem ... i thinkk

[mild orbit]

the answer is 0. Divide by x^4 the numerator and denominator

[harsh harbor]

alright thanks guys

[hazy ore]

Never done infinite limits before, but I thought "eh why not", this mess is the first thing that came to mind. This a bad idea?

Specifically tried it here but didn't get anywhere

But this is less about the question and more about "is this a bad method to find infinite limits with" ig

[ivory trout]

HELP

[grizzled osprey]

okay guys, i have a word problem that i’m really struggling with.. Two brothers, Mark and Steven, each inherit $45000
$⁢45000. Mark invests his inheritance in a savings account with an annual return of 3.2%
3.2%, while Steven invests his inheritance in a CD paying 4.5%
4.5% annually. How much more money than Mark does Steven have after 1
1 year?

[grizzled osprey]

is this just to be simplified ?

[ivory trout]

yes

[grizzled osprey]

if i’m not mistaken, you’re gonna wanna transform the expression, what would make it x squared -8 over 2x, and then for the bottom 3 over x-2.. so then you’re gonna wanna simply it, which makes it come down to x cubed -2x squared -8x+16 over 6x

[grizzled osprey]

sorry i’m not very good at explaining but that’s the best way i can explain

[ivory trout]

Thats very confusing

[grizzled osprey]

final answer should look like this

[ivory trout]

I’m like a visual learner

[grizzled osprey]

let me see if i can write it out

[ivory trout]

Okay thank you so much

[willow bear]

@grizzled osprey don't give out answers

[grizzled osprey]

oh sorry i was just trying to work through and explain it lol

[ivory trout]

I have the answer already

I don’t know how to get there

[willow bear]

well the first step would be to rewrite the denominator of your big fraction into 3/(x-2)

[ivory trout]

I’m lost

this?

[willow bear]

yes, the 2/(x-2) + 1/(x-2)

[ivory trout]

Yes what about it

combine tic

it?

[willow bear]

yes that's what i said to do

[ivory trout]

Okay then after that

I have to make the denominator on top the same right

[willow bear]

combine the two fractions on top too yes

was going to suggest that anyway

[grizzled osprey]

do you mind helping me with a word problem

[ivory trout]

how

the LCD right

[willow bear]

add the fractions as you normally would

[ivory trout]

u can’t subtract

They have to have same denominator

[willow bear]

open a help channel. idk if i will be the one to help you there

[grizzled osprey]

i’m new to using this, how do i do that?

[willow bear]

read #❓how-to-get-help for instructions

[ivory trout]

i got this

@willow bear

[willow bear]

incorrect

[ivory trout]

What did i do wrong

[willow bear]

x/2 - 4/x is not just x^2-8

[ivory trout]

I’m so lost

how do i subtract the two then

I keep getting the same thing

[willow bear]

don't forget about the denominator

$\frac{x}{2} - \frac{4}{x} = {\color{red}\frac{{\color{black}x^2-8}}{2x}}$

[obsidian monolith]

Ann

[ivory trout]

Ohh

Then what

[willow bear]

well now you have a fraction divided by a fraction

$\frac{x^2-8}{2x} \bigg/ \frac{3}{x-2}$

[obsidian monolith]

Ann

[ivory trout]

yup i have that as well

what do i do from there

[willow bear]

do you know how to divide fractions?

[ivory trout]

Reciprocal right,

You multiply

[willow bear]

you multiply the first fraction by the reciprocal of the second, yes

and do you know how to multiply fractions?

[ivory trout]

Okay let me do that

Yes

I got the answer

This exactly

Thank you

[warped cliff]

what is the best book for calculus

[coarse fog]

Schaums

[viscid thistle]

quick assistance needed in #help-3 I know its simple and I'm doing something wrong somewhere stupidly

[strong topaz]

in how many ways can there be 4 odd and 3 even digits in a 7 digit number and repitition is allowed and the digits must be from 0-9

[fervent wyvern]

6C33C35^45^3+6C42C25^45^2*4 I guess

By dividing two cases one is odd number for the largest digit and one is even because no 0 in the largest digit

[fervent wyvern]

2500000 I guess

[fervent wyvern]

Rudin also

It can be used as refrence book

[modest cypress]

i cant find the center

[modest cypress]

can someone help me find the c

[high willow]

Does anyone possibly know how to solve this

[oblique gazelle]

@high willow This is just trigonometry

Make a triangle with a height of 24 and an angle of 34 degrees in the top left/right

Solve for the hypotenuse

[high willow]

Thank you! I completed the question I think it’s right

[oblique gazelle]

No problem

[brisk pasture]

Idk how to answer this

[oblique gazelle]

Well, domain is all the x-values that are valid for the function

And the arrow indicates the function continues forever in that direction

[brisk pasture]

It wouldn't be [-8, infinity)?

-infinity*

[oblique gazelle]

It would be (-infinity, -8]

Also known as x <= -8

[brisk pasture]

But isn't -8 an x value?

[oblique gazelle]

Yes

Hence the less than or equal to sign

[brisk pasture]

Shouldn't the x value go first?

[oblique gazelle]

The x <= -8 is correct, but the -infinity to -8 is because -infinity is less than -8

Infinitely less one might say

The lower value goes first

[brisk pasture]

Oh ok thanks

Would this be (0,-infinity)U(7,infinity)?

[viscid thistle]

Something prolly easy factoring I probably can’t see and I screwed up #help-13

[oblique gazelle]

@brisk pasture Sorry, I left for a bit, but that domain could simply be written as "x is not 7"

As every other value for x is valid

[brisk pasture]

Oh it's fine,n@oblique gazelle and I got it thank you anyways!

[wide bramble]

hey im pretty new to trig and i dont get what a coterminal angle is

[vapid plaza]

Is there something in particular that confuses you

[wide bramble]

well i dont understand the unit circle at a whole ig

[vapid plaza]

You might want to be more specific than that

[willow bear]

coterminal angles are angles which differ by a whole number of full turns

[brisk pasture]

The range would be {y|0<y≤7} right?

[willow bear]

sure would.

[brisk pasture]

Ok thanks

[strong topaz]

If a set X contains exactly 7 elements and set B contains 5 elements then what is the number of onto functions from X to Y?

there are two ways we can form groups and then map them with the elements of Y 1-1-1-1-3 or 1-1-1-2-2 now from the first way we can form groups in 7C4 * remaining 3 numbers we need to form them in a group of 3 so 3C3 or 1+ 7C3 * 4C2* 2C2 all of this then multiplied by 5! the answer should be 29400 but it isn't why? What did I do wrong?

[strong topaz]

<@&286206848099549185>

[brisk pasture]

How is the domain not all real numbers?

[raw hill]

Consider $g(x)=\sqrt{x+2}$ when $x+2<0$.

[obsidian monolith]

Civil Service Pigeon

[brisk pasture]

@raw hill so I'm not finding the domain of (f o g)(x)=x+6?

[raw hill]

the point is that when $g(x)$ isn't defined for the reals the entire composition essentially goes "poof"

[obsidian monolith]

Civil Service Pigeon

[raw hill]

cause when you simplify like that you assume the domain isn't an issue

but also $\sqrt{x^2 +6} \neq x+6$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

so it's not like that matters here anyway

[brisk pasture]

@raw hill so I'm just finding the domain of √x+2?

[raw hill]

yes.

[brisk pasture]

Ok thanks

[dry fractal]

When using ∑ to expand (a+b)^n, how do you find specific terms without needing to expand the whole equation? For example if I wanted to know all numbers that are coefficients of a^5b^4 in (3a-b/3)^9

[fallen saddle]

I’m having trouble with this question

These are the answers from the back of my text book

Just not sure how they were derived.

[brisk pasture]

(f(g(x) would be x right? But how would I do (g(f(x)?

[ashen skiff]

$alog_2(x) + k$, plug in your x values. $alog_2(\frac{1}{4}) + k$ and $alog_2(16) + k$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

You should end up with $a(-2) + k = -9$ and $a(4) + k = -6$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

then just solve from there

[ashen skiff]

g(f(x)) = $\frac{\frac{x-1}{x}}{\frac{x-1}{x}-\frac{x}{x}}$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

All terms are divided by x, so we can just swoop through and remove those

And you're left with

$\frac{x-1}{x-1-x}$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

🍞 Is Toast Modern? 🍞

[ashen skiff]

or just -x+1

[brisk pasture]

@ashen skiff would f(g)(x)=x?

[ashen skiff]

Only if f(x) and g(x) are inverses

f(g(x)) = $\frac{\frac{x}{x-1}-1}{\frac{x}{x-1}}$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

And then solve

[dry fractal]

cough

[fallen saddle]

How is it possible to have two different variable and still solve?

[ashen skiff]

I'm not sure exactly what you're asking, but I think you would use pascal's triangle

[dry fractal]

substitution?

[dry fractal]

there was an algebraic way

[ashen skiff]

System of equations. Subtract one equation from another

$a(-2) + k = -9$ and $a(4) + k = -6$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

subtract the left sides and the right sides, you get \ $-2a + k - 4a - k = -9 - (-6)$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[brisk pasture]

@ashen skiff just by knowing g(f)(x), you know they're not inverses right?

[ashen skiff]

The k's cancel out and you can solve for a

[ashen skiff]

Correct

[brisk pasture]

Ok thanks

[ashen skiff]

The only way I know would be pascal's triangle

[dry fractal]

how would I use pascal's triangle to find that?

[ashen skiff]

The numbers of the triangle represent the coefficients.
(a+b)^0 = 1, and 1 is the first layer
(a+b)^1 = 1a+1b, and 1, 1 is the second layer
(a+b)^2 = 1a^2 + 2ab + 1b^2, and 1, 2, 1 is the third layer
(a+b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3, and 1, 3, 3, 1 is the fourth layer

I'm assuming that's what you were asking with the original question but I'm not totally sure

[dry fractal]

yea

I guess that works too

[ashen skiff]

So, using pascal's triangle, if you wanted (a+b)^9, you'd know to look at the 10th layer and that'll give you the coefficients

[sturdy bobcat]

if i need to find the derivative dZ/dt when $Z = (u^2-1)^3$ and $u = t^3$ . is this the same as just finding the derivative of $Z = ((t^3)^2-1)^3$ ?

[obsidian monolith]

zeffs

[ashen skiff]

The derivative of $(u^2-1)^3$ is $6u(u^2-1)^2$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[sturdy bobcat]

what about t?

[ashen skiff]

Replacing $u$ with $t^3$ would give you $6t^3((t^3)^2-1)^2$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

Which means it's not the same

[sturdy bobcat]

but u = t^3 so

why would i need that info if im not gonna use it and just use the variable u

[ashen skiff]

because the question is asking for dZ/dt, not dZ/du

you have to find dZ/du first, then convert that into dZ/dt by multiplying by du/dt

[sturdy bobcat]

my book says the derivative is $18t^5(t^6-1)^2$

[obsidian monolith]

zeffs

[ashen skiff]

yup, i'm totally wrong, my way is longer and dumber

you can just replace u with t^3

[sturdy bobcat]

oh okay, so my first intuition was correct?

[ashen skiff]

yes

[strong topaz]

how to solve this?

[viscid thistle]

Can anyone solve this integral
xarctan(x)

[ashen skiff]

Seems like you'd use integration by parts

[viscid thistle]

I used it but it gives zero at other side of equality and some value at another
I don't know now what to do
Can you please send me solution

[ashen skiff]

$\int udv = uv - \int vdu$

$u=arctan(x), dv=x, du=1/(x^2+1), v=x^2/2$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[ashen skiff]

@viscid thistle

[viscid thistle]

@ashen skiff what is the final answer, because I already used this method but not getting any result

[viscid thistle]

most important part of complex numbers for problem solving?

[brisk pasture]

I think it would be h(5)= 0 or 75

K(5)

[echo mortar]

can i get help on a math question i have?

i have part of the answer, but i dont know what i am missing

i thought i got everything, but apparently not

[ashen skiff]

Can you show your work?

[echo mortar]

i also use a unit circle

i dont know what it is i am missing

i watched the video and they did the same thing

[oblique gazelle]

Yes, h(5) is 75

[ashen skiff]

Ah, here's your issue

you wrote -1.43, which isn't in the domain they gave you

you'll have to find the coterminal angle that's between 0 and 2pi

[brisk pasture]

Can you explain how? I think I know why but I want to make sure my reasoning is correct

Just because x=5 is y=75?

Or is there something more

[oblique gazelle]

So, when I plug 5 into the function, I am now looking at 5 on the x-axis

[echo mortar]

@ashen skiff so do i just take the 1.43 and subtract or add 2pi to it?

[ashen skiff]

-1.43 + 2pi

[oblique gazelle]

75 is the y-value on the graph that corresponds to 5 on the x-axis

[brisk pasture]

Oh wow, that's surprisingly simple, thank you

[echo mortar]

@ashen skiffso i still use the -1.43, but because it isnt in the circle, i have o find its reference angle, which should be in the circle

[oblique gazelle]

If you plugged 5 into the equation of this graph you would get 75

Np

[ashen skiff]

correct

[echo mortar]

oh huh, that makes a lot of sense, tyty, idk how the video got the right answer if theyh didnt do that

thank you\

[narrow zephyr]

Not sure how to do this

[hollow owl]

Me neither

[ashen skiff]

You can really just use guess and check.

e^7 * 0.05 = 54.831658

So at what term is (1/1)+(7/1)+(49/2)... greater than 54.831?

[narrow zephyr]

i know that epsilon is 2

there is easier way to do it

but i wanna know if this way is also viable

i tried log maclurin expansion

but it does not work becasue i have that n!

[ashen skiff]

I don't think theres really any defined way to do it

[narrow zephyr]

maybe

[noble hollow]

so before i study precalc do you guys have a list of things i need to master or learn? i didnt really learn during my jhs years the school system in my country sucks i need to be more independent

[uncut mulch]

basic algebra

coordinate geometry, equations of lines, systems of equations

quadratics

if you have a decent understanding of those, you shouldn't have that much issue with the new stuff introduced in precalc

[noble hollow]

do you guys have learning modules for studying conic sections? even after watching chemistry tutor i still have a questions

[viscid thistle]

can someone please explain how he found the turning point with differentiated AB^2 and not AB or didn't atleast square root it at the end?

[vapid plaza]

If AB is at its minimum, then AB^2 must be at its minimum as well.

[low isle]

hi everyone. is this channel a place to ask question for vector math?
i need to figure out what is a dot product, but I can't understand. my current definition of it pretty much contradicts what vectors are and properties of geometric lines (that are vectors, more-or-less) in general

I'm not working on a homework or something, I don't have a "task" that I need to "solve", so i'm not sure if #help-x is the place.

I'm working on a computer program (so-to-say) and it can calculate dot product automatically (programming language has the required function), but that's of no use to me until I figure out what does it do.

[surreal swift]

what exactly is the problem?

[low isle]

I don't understand what is "dot" product. What exactly does it mean.

so far the best definition i could get is "how much does 1 vector overlap the 2nd", but if vectors intersect, then they do that in 1 specific point

whether it's 3D space or 2D space

The result of dot product operation is scalar

and how can be vector operation result in a scalar value?

the only thing scalar values can define in vectors is their length (magnitude), as far as I understand.

only thing I need at this moment is to gain understanding of what does dot product represent and why is it scalar

[vapid plaza]

Why not?

[low isle]

well, it makes sense when you get the length of the vector. but for the rest of operations?

[summer ruin]

dot product represents how similar are the directions in which certain vectors are pointing

positive if they're similar, zero if they're orthogonal and negative if they're pointing in different directions

[low isle]

hmm.

well, now that i think about it, it does make some sense.

[uncut nacelle]

when you are transforming a function how do you identify a horizontal shift ?

for vertical shift it's pretty clear that f(x)+C (some constant) is there to decide weather the function is shifting up or down (nvm got it)

[uncut nacelle]

you check how the function is evaluated, for eg: f(x) = (x-2)3 + 2, here the function has been evaluated as f(x-2) = 3x + 2, there's vertical shift and horizontal shift both in the function, original function is just f(x)=3x

[viscid thistle]

Yeah but aren’t you supposed to square root t because it’s squared?

[oak valley]

I need help. Im completely lost. Im at inverse trigonometry and I have no clue what im supposed to do

I dont have the time to go to my campus' math help group, and the test is due by tommorow at midnight and i am way behind

How do i find this

I genuinely do not understand how i am supposed to find that without an existing graph, and i dont know how to ask my calculator this.

[hushed sphinx]

Ahem, do you mean this is a test rather than homework? We don't allow cheating.

[oak valley]

No

This is homework

Im studying for a test that is due by midnight tommorow

This is homework for LAST WEEKs test.

[hushed sphinx]

Hopefully you have a table of values of trig functions for simple "standard" angles somewhere. There's not really any computation you can do to progress here (if you want an exact result, which you do), you just have to know it.

Or, perhaps, if you know which angle has a tangent of sqrt(3), subtract that from pi/2.

Or even more perhaps, remember that the only "nice" angles between 0 and pi/2 that have "nice" values of the trig functions are pi/6, pi/4, and pi/3, and then work out the cotangent of each of those to see if it makes sqrt(3).

[oak valley]

Gotcha

That helps

[hushed sphinx]

... which is, strictly speaking, a lie, because cos(pi/5) = (1+sqrt(5))/4 is arguably also nice.

[vapid plaza]

The minimum of AB^2 will indeed be the square of the minimum of AB, but the turning point (the t at which minimum occurs) is the same

[viscid thistle]

Wait why is it the same?

[vapid plaza]

Bruh🤓

Think of t as the “time”. So when AB is at minimum, that’s the same time as when AB^2 is at minimum

[viscid thistle]

No I get that part

I just don’t get why the actual NUMBER is the same

[willow bear]

the number isn't the same, but the time at which it occurs is

[left orchid]

10 is 8 away from 2
the max of f'(x) is 2
so if every point between 2 and 10 has a slope of 2,
max val for f(10) would be f(2) + 2*8 = 21
the min of f'(x) is -1
so if every point between 2 and 10 has a slope of -1,
min val for f(10) would be f(2) - 1*8 = -3
so -3 <= f(10) <= 21

[viscid thistle]

what year group is pre uni?

[hushed sphinx]

It's not a year group -- just mathematical topics that are most often taught in school levels prior to university.

[viscid thistle]

ah right ok

[tired epoch]

Are you from the US?

[viscid thistle]

yh

[tired epoch]

So up to 12th grade I think

[viscid thistle]

ohh ok

[hushed sphinx]

The same topic can be taught at different levels in different countries and school systems. Please don't take the category headings as more than a rough guide to where the channel you need it most likely located.